There was a thread where we discussed adding a bandana under or over a ball cap, so that is one way to test that design.

The ball cap variations are light, compact and usually less expensive. Wide brimmed hats with a vented crown will give more cooling, like hauling your own shade. The Sunday Afternoon Adventure hat does it all and are quite light. The neck cape works well with a backpack sticking up behind. Ugly enough to be first level birth control, but effective :)

I keep forgetting the Kavu Chilba, which can double as a rain hat. Surpassed only by the Sunday Afternoons hat for quirky good looks ;)

A GoLite Chrome Dome umbrella is a option too, cooling your whole upper body, good for rain and a partial shield for one end of a tarp.

I too like the sunrunner, with the French Foreign legion (or Ferengi?) neck flap attached.

A couple of reasons I haven't heard mentioned already:

On a longer trip where one goes into towns for resupply, I like being able to remove the neck flap and turn it into a more conventional looking baseball hat. Yes, I shouldn't concern myself with "looks", but my theory is that if I can clean up a bit and look less like a hobo, I might get treated a little better (?) and perhaps it will be easier to hitch a ride that way. Who knows for sure.

Another advantage over a wide brimmed hat is that a coat or poncho hood fits comfortably over it when there's wind-driven rain (or sleet or snow).

I've logged a lot of miles with my OR sunrunner; I actually bought a second one when the fabric of the first started getting thin/worn enough that I was getting tanned on my bald head under the hat. That took a good deal of miles & time, however, I don't mean to say that durability is a problem in normal use. I'm just saying that after quite a lot of use I'm still a fan.

Oh, one other thing it has over some types of wide-brimmed hat --- it can be put into a mode where you essentially have a chinstrap so that it won't blow off in high wind. In that mode, just the neck flap alone helps a lot when cold wind is blowing by your ears. And then it can be changed to wear it in a more "easy on, easy off" mode.

I ended up ordering both on Amazon last night, and will test them out on this trip. But based on this thread, I'm think that the full brimmed Sobriolet will work best for the desert heat/low wind situations I'll be experiencing on this trip, and the SunRunner will be great for the cooler temps/intense high altitude sun/windy passes and ridge walking on my SEKI hike at the end of July. Plus my black(what was I thinking?) REI ballcap is getting kind of ratty after 4 years and even with sunblock I've gotten kind of burned in the spots where it sweated off the last couple years. The Sunrunner will be great for trail running as well.

Just another case of admitting to myself there isn't one perfect piece of do-it-all gear for every scenario